Width of the rectangle is 12 cm.
Solution:
The length of a rectangle is 4 cm more than its width , and the area of the rectangle is 96 cm². Find the width of the rectangle.
Given data:
Let x be width of the rectangle.
Length of the rectangle = (x + 4) cm
Area of the rectangle = 96 cm²
length × breadth = 96
![(x+4)\times x =96](/tpl/images/0558/8923/d465c.png)
![x^2+4x=96](/tpl/images/0558/8923/5937d.png)
Subtract 96 from both sides.
![x^2+4x-96=0](/tpl/images/0558/8923/6ecdb.png)
Let us factor the polynomial.
![x^2+8x-12x-96=0](/tpl/images/0558/8923/5f92a.png)
Take x common in 1st two terms and -12 common in next two terms.
![x(x+8)-12(x+8)=0](/tpl/images/0558/8923/150bc.png)
Now, take (x + 8) common in both terms.
![(x+8)(x-12)=0](/tpl/images/0558/8923/8b65b.png)
x + 8 = 0 and x - 12 = 0
x = -8 and x = 12
Dimension cannot be in negative terms, so ignore x = -8.
Width = 12 cm
Width of the rectangle is 12 cm.